To exploit the vast amount of sequence information provided by the Genomic revolution, the biological function of these sequences must be identified. As a practical matter, this is often accomplished by functional inference. Purely sequence-based approaches, particularly in the "twilight zone" of low sequence similarity levels, are complicated by many factors. For proteins, structure-based techniques aim to overcome these problems; however, most require high-quality crystal structures and suffer from complex and equivocal relations between protein fold and function. In this study, in extensive benchmarking, we consider a number of aspects of structure-based functional annotation: binding pocket detection, molecular function assignment and ligand-based virtual screening. We demonstrate that protein threading driven by a strong sequence profile component greatly improves the quality of purely structure-based functional annotation in the "twilight zone." By detecting evolutionarily related proteins, it considerably reduces the high false positive rate of function inference derived on the basis of global structure similarity alone. Combined evolution/structure-based function assignment emerges as a powerful technique that can make a significant contribution to comprehensive proteome annotation.